cp's OEIS Frontend

A368498 a(n) is the smallest number that can be written in exactly n ways as the sum of positive integer powers of its distinct prime factors, or -1 if no such number exists.

%I A368498 #17 Dec 31 2023 10:23:45
%S A368498 1,2,30,270,2730,4290
%N A368498 a(n) is the smallest number that can be written in exactly n ways as the sum of positive integer powers of its distinct prime factors, or -1 if no such number exists.
%C A368498 a(6) > 33000000 if it exists.
%C A368498 a(7) = 5195190.
%e A368498 a(3) = 270 because the distinct prime factors of 270 are 2, 3, 5, and 270 = 2^1 + 3^5 + 5^2 = 2^6 + 3^4 + 5^3 = 2^8 + 3^2 + 5^1 can be written in exactly 3 ways as the sum of positive integer powers of 2, 3 and 5.
%p A368498 f:= proc(n) local P,S,p,i;
%p A368498   P:= numtheory:-factorset(n);
%p A368498   S:= mul(add(x^(p^i),i=1..floor(log[p](n0)),p=P);
%p A368498 coeff(S,x,n);
%p A368498 end proc:
%p A368498 V:= Array(0..4): count:= 0:
%p A368498 for n from 1 while count < 5 do
%p A368498 v:= f(n):
%p A368498   if V[v] = 0 then V[v]:= n; count:= count+1 fi;
%p A368498 od:
%p A368498 convert(V,list);
%Y A368498 Cf. A366914.
%K A368498 nonn,more
%O A368498 0,2
%A A368498 _Robert Israel_, Dec 27 2023